Borsuk-Ulam Theorem

The Borsuk-Ulam Theorem is another amazing theorem from topology.  An informal version of the theorem states that at any given moment on the earth's surface, there exists two antipodal points on exactly opposite sides of the earth with the same temperature and barometric pressure.

More formally, assuming that temperature and barometric pressure are continuous functions, the theory says that any continuous function from an n-sphere to Rⁿ must send a pair of antipodal points to the same point.